Calculating the density of states for large‐scale molecular systems

Abstract

We present a new method for calculating the density of states of large‐scale molecular systems. The new algorithm does not require calculation of all eigenvalues of the force constant matrix. The histogram for the eigenvalue distribution is constructed by performing a sequence of sparse LDLT matrix factorizations. Moreover, the entire calculation can be fully parallelized on a multiprocessor computer system.

An Efficient Algorithm for Calculating the Heat Capacity of a Large-Scale Molecular System

“…Notice that a 100-point Gaussian quadrature calculation for pe12k took a little over 100 seconds. This is at least a hundred times faster than our earlier approach [10] which took several hours.…”

“…These factorizations must be carried out in a numerically stable manner using the Bunch and Kaufman [9] technique to ensure a reliable inertia count. It has been shown [10] that the computational procedure based on LDL T factorization and inertia count is considerably faster than the brute-force approach of computing all eigenvalues of F. In this paper, we introduce another way of computing C v . The new algorithm does not rely on treating the molecular system as a continuum.…”

Normal Coordinate Analysis for Polymer Systems: Capabilities and New Opportunities

“…We have found that calculating a time-averaged Hessian matrix over several thousand steps of an MD simulation and diagonalizing this averaged matrix eliminates this difficulty. [110][111][112][113][114] Trajectory averaged NCA studies have so far been performed mostly on reasonably simple model systems-united atom polyethylene crystals and droplets (or pairs of droplets) with up to 36 000 atoms, as shown in Figure 6. The droplets serve as model systems for sub-micron polymer particles recently produced by Barnes and coworkers.…”

“…It is found that for the particle, but not for the crystal, that the lower-frequency modes and eigenvalue spacings exhibit random behavior and the higher frequency modes do not. [112] High-and low-frequency eigenvectors also exhibit random behavior with respect to perturbations of the matrix. Several high-and low-frequency eigenvectors were computed for a series of Hessian matrices into which a random perturbation was gradually introduced.…”